Abstract: The present paper introduces a combinatorial trigonomet ric polynomial operator Sn(f;r,θ) (where r is a given natural number) based on the values of f(θ) (where f(θ)∈C2π〖KG*2〗and f(θ ) is an odd function) with the nodes θ_k=kπ/(n+1)ⁿ _k=1. It has been proved that S_n(f;r,θ) uniformly converges to f(θ) (f(θ)∈C2π and f(θ) is an odd function) on the total real axis. And Sn(f;r,θ) reaches the best approximation order when used to approxim ate to f(θ) where f(θ)∈Cj2π (0≤j≤r-1) and f(θ) is an odd function.

Key words: combinatorial trigonometric interpolation polynomial, u niform convergence, best convergence order